$K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 9x + 4$ and $ KL = 3x + 52$ Find $JL$.
Answer: A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {9x + 4} = {3x + 52}$ Solve for $x$ $ 6x = 48$ $ x = 8$ Substitute $8$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 9({8}) + 4$ $ KL = 3({8}) + 52$ $ JK = 72 + 4$ $ KL = 24 + 52$ $ JK = 76$ $ KL = 76$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {76} + {76}$ $ JL = 152$